Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31771258 | C2 | semidirect |
| 2. D4×D1076 | C2 | semidirect |
| 3. #31770953 | C2 | semidirect |
| 4. #31770920 | C2 | semidirect |
| 5. #31770842 | C2 | semidirect |
| 6. #31770801 | C2 | semidirect |
| 7. #31770740 | C2 | semidirect |
| 8. C4×#16864387 | C2 | semidirect |
| 9. #31770670 | C2 | semidirect |
| 10. #102×D269 | C2 | semidirect |
| 11. #474×C269 | C2 | semidirect |
| 15. C2×D2152 | C22 | semidirect |
| 17. C2×C8×D269 | C22 | semidirect |
| 22. #22575428 | C22 | semidirect |
| 26. C4×D1076 | C22 | semidirect |
| 27. C4⋊C4×D269 | C22 | semidirect |
| 28. #22575386 | C22 | semidirect |
| 29. #22575375 | C22 | semidirect |
| 31. #22575373 | C22 | semidirect |
| 32. #22575373 | C22 | semidirect |
| 33. #22575373 | C22 | semidirect |
| 34. #22575365 | C22 | semidirect |
| 35. C4×#14524130 | C22 | semidirect |
| 36. C4⋊Q8×C269 | C22 | semidirect |
| 38. #107×C269 | C22 | semidirect |
| 39. C4⋊C8×C269 | C22 | semidirect |
| 92. D1076 | D8 | semidirect |
| 105. D4×C269 | #41 | semidirect |
| 142. C269 | #3294 | semidirect |
| 148. #474 | D269 | semidirect |
| 161. C4⋊Q8 | C2×D269 | semidirect |
| 174. #107 | C2×D269 | semidirect |
| 175. C4⋊C8 | C2×D269 | semidirect |
| 240. D4 | #16864403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771258 | 2 |
| D4×D1076 | 2 |
| #31770953 | 2 |
| #31770920 | 2 |
| #31770842 | 2 |
| #31770801 | 2 |
| #31770740 | 2 |
| C4×#16864387 | 2 |
| #31770670 | 2 |
| #102×D269 | 2 |
| #474×C269 | 2 |
| #3294 | 269 |